WARNING: Excluded non-linear constraints:[E=5*A+C*C,A+1=<B*B]

Preprocessing Cost Relations
=====================================

#### Computed strongly connected components 
0. recursive  : [l1/5,l2/5]
1. non_recursive  : [exit_location/1]
2. recursive  : [l3/4]
3. non_recursive  : [l3_loop_cont/2]
4. non_recursive  : [l1_loop_cont/7]
5. non_recursive  : [l0/6]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into l1/5
1. SCC is completely evaluated into other SCCs
2. SCC is partially evaluated into l3/4
3. SCC is completely evaluated into other SCCs
4. SCC is partially evaluated into l1_loop_cont/7
5. SCC is partially evaluated into l0/6

Control-Flow Refinement of Cost Relations
=====================================

### Specialization of cost equations l1/5 
* CE 2 is refined into CE [10] 
* CE 5 is refined into CE [11] 
* CE 3 is refined into CE [12] 
* CE 4 is refined into CE [13] 


### Cost equations --> "Loop" of l1/5 
* CEs [12] --> Loop 10 
* CEs [13] --> Loop 11 
* CEs [10] --> Loop 12 
* CEs [11] --> Loop 13 

### Ranking functions of CR l1(X,Y,Z,A1,B1) 

#### Partial ranking functions of CR l1(X,Y,Z,A1,B1) 
* Partial RF of phase [10,11]:
  - RF of loop [10:1]:
    Y
  - RF of loop [11:1]:
    -X+4


### Specialization of cost equations l3/4 
* CE 9 is refined into CE [14] 
* CE 8 is refined into CE [15] 


### Cost equations --> "Loop" of l3/4 
* CEs [15] --> Loop 14 
* CEs [14] --> Loop 15 

### Ranking functions of CR l3(A,B,C,Z) 

#### Partial ranking functions of CR l3(A,B,C,Z) 


### Specialization of cost equations l1_loop_cont/7 
* CE 7 is refined into CE [16,17,18] 
* CE 6 is refined into CE [19] 


### Cost equations --> "Loop" of l1_loop_cont/7 
* CEs [17] --> Loop 16 
* CEs [16] --> Loop 17 
* CEs [19] --> Loop 18 
* CEs [18] --> Loop 19 

### Ranking functions of CR l1_loop_cont(A,B,C,D,E,F,G) 

#### Partial ranking functions of CR l1_loop_cont(A,B,C,D,E,F,G) 


### Specialization of cost equations l0/6 
* CE 1 is refined into CE [20,21,22,23,24,25,26] 


### Cost equations --> "Loop" of l0/6 
* CEs [23,26] --> Loop 20 
* CEs [22,25] --> Loop 21 
* CEs [21,24] --> Loop 22 
* CEs [20] --> Loop 23 

### Ranking functions of CR l0(X,Y,A,B,C,Z) 

#### Partial ranking functions of CR l0(X,Y,A,B,C,Z) 


Computing Bounds
=====================================

#### Cost of chains of l1(X,Y,Z,A1,B1):
* Chain [[10,11],13]: 1*it(10)+1*it(11)+0
  Such that:it(11) =< -X+4
it(10) =< Y

  with precondition: [Z=2] 

* Chain [[10,11],12]: 1*it(10)+1*it(11)+0
  Such that:it(11) =< -X+4
it(11) =< -X+A1
it(10) =< Y-B1

  with precondition: [Z=3,B1>=1,A1>=X,Y>=B1,Y+A1>=X+B1+1] 

* Chain [13]: 0
  with precondition: [Z=2] 

* Chain [12]: 0
  with precondition: [Z=3,A1=X,Y=B1,Y>=1] 


#### Cost of chains of l3(A,B,C,Z):
* Chain [[14]]...: 1*it(14)+0
  with precondition: [A>=1,Z=2] 

* Chain [[14],15]: 1*it(14)+0
  with precondition: [Z=2,A>=1] 

* Chain [15]: 0
  with precondition: [Z=2] 


#### Cost of chains of l1_loop_cont(A,B,C,D,E,F,G):
* Chain [19]...: 1*s(3)+0
  with precondition: [A=3,D>=1] 

* Chain [18]: 0
  with precondition: [A=2] 

* Chain [17]: 0
  with precondition: [A=3] 

* Chain [16]: 1*s(4)+0
  with precondition: [A=3,D>=1] 


#### Cost of chains of l0(X,Y,A,B,C,Z):
* Chain [23]: 1*s(5)+1*s(6)+0
  Such that:s(6) =< Y

  with precondition: [] 

* Chain [22]: 1*s(7)+1*s(8)+0
  Such that:s(8) =< Y

  with precondition: [Y>=1] 

* Chain [21]: 3*s(9)+1*s(11)+0
  Such that:s(11) =< Y

  with precondition: [Y>=1,A>=1] 

* Chain [20]...: 3*s(13)+1*s(15)+0
  Such that:s(15) =< Y

  with precondition: [Y>=1,A>=1] 


Closed-form bounds of l0(X,Y,A,B,C,Z): 
-------------------------------------
* Chain [23] with precondition: [] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [22] with precondition: [Y>=1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [21] with precondition: [Y>=1,A>=1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [20]... with precondition: [Y>=1,A>=1] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of l0(X,Y,A,B,C,Z): inf 
Asymptotic class: infinity 
* Total analysis performed in 59 ms.

